A256472 Primes p for which there are exactly as many primes in the range [p^2, p*nextprime(p)] as there are in the range [p*nextprime(p), nextprime(p)^2], where nextprime(p) gives the next prime after prime p.
2, 29, 43, 59, 71, 463, 601, 881, 1049, 1103, 1171, 1451, 2311, 2591, 2689, 2693, 2777, 3083, 3089, 3917, 8543, 12889, 13007, 13799, 13873, 13877, 15497, 18457, 19477, 20369, 23017, 25073, 26641, 29179, 32801, 33757, 35327, 41647, 43987, 46279, 47041, 49211, 51577, 63113
Offset: 1
Keywords
Examples
For p=2, we have in the range [2*2, 2*3] just one prime {5}, and also in the latter range [2*3, 3*3] just one prime {7}, thus 2 is included in the sequence.
Programs
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Mathematica
Select[Prime@ Range@ 500, Count[Range[#^2, # NextPrime[#]], ?PrimeQ] == Count[Range[# NextPrime[#], NextPrime[#]^2], ?PrimeQ] &] (* Michael De Vlieger, Mar 30 2015 *)
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Scheme
(define (A256472 n) (A000040 (A256471 n)))
Comments